Ferromagnetism and superconductivity are in most cases adverse. However,
recent experiments reveal that they coexist at interfaces of LaAlO$_{3}$ and
SrTiO$_{3}$ [1]. We analyze the ferromagnetic state within density
functional theory and provide evidence that it is also generated by Ti 3d
interface electrons, as is the two-dimensional electron liquid at the
interface which gives rise to superconductivity [2]. We demonstrate that
oxygen vacancies in the TiO$_{2}$ interface layer enhance the tendency for
ferromagnetism considerably. This allows for the notion that areas with
increased density of oxygen vacancies produce ferromagnetic puddles and
account for the previous observation of a superparamagnetic behavior in the
superconducting state [3].\\[4pt]
[1] Lu Li, C.Richter, J.Mannhart, and R.C.Ashoori, Nature Physics 7, 762 (2011).\\[0pt]
[2] N. Reyren et al., Science 317, 1196 (2007).\\[0pt]
[3] N.Pavlenko, T.Kopp, E.Y.Tsymbal, G.A.Sawatzky, and J.Mannhart, cond-mat/arXiv:1105.1163 (2011)